Quaternionic Aharonov–Bohm Effect

A quaternionic analog of the Aharonov–Bohm effect is developed without the usual anti-hermitian operators in quaternionic quantum mechanics. A quaternionic phase links the solutions obtained to ordinary complex wave functions, and new theoretical studies and experimental tests are possible for them.

References(21)

Figures(0)

[1]

Peres experiment using photons: No test for hypercomplex (quaternionic) quantum theories

Stephen L. Adler
(
- Princeton, Inst. Advanced Study
)

- Phys.Rev.A 95 (2017) 6, 060101
•
e-Print:
- 1604.04950
•
DOI:
- 10.1103/PhysRevA.95.060101

[2]

: Quaternionic Quantum Mechanics and Quantum Fields. Oxford University Press, Oxford

S.L. Adler

[3]

GEOMETRY OF YANG-MILLS FIELDS

M.F. Atiyah

- Pisa, Italy: Sc. Norm. Sup. ( 1979) 98 P. ( Lezioni Fermiane)

[4]

Experimental status of quaternionic quantum mechanics

S.P. Brumby
(
- Melbourne U.
)
,
Girish C. Joshi
(
- Melbourne U.
)

- Chaos Solitons Fractals 7 (1996) 747-752
•
e-Print:
- quant-ph/9610009
•
DOI:
- 10.1016/0960-0779(95)00001-1

[5]

Quaternionic Dirac equation

A.J. Davies
(
- Melbourne U.
)

- Phys.Rev.D 41 (1990) 2628-2630
•
DOI:
- 10.1103/PhysRevD.41.2628

[6]

Nonrelativistic quaternionic quantum mechanics in one dimension

A.J. Davies
(
- Melbourne U.
)
,
B.H.J. McKellar
(
- Melbourne U.
)

- Phys.Rev.A 40 (1989) 4209-4214
•
DOI:
- 10.1103/PhysRevA.40.4209

[7]

: Observability of quaternionic quantum mechanics

A.J. Davies
,
B.H.J. McKellar

- Phys.Rev.A 46 (1989) 3671-3675

[8]

Quaternionic Dirac Scattering

Stefano De Leo
(
- Campinas State U.
)
,
Gisele Ducati
(
- ABC Federal U.
)
,
Sergio Giardino
(
- Campinas State U.
)

- J.Phys.Math. 6 (2015) 1, 1000130
•
e-Print:
- 1505.01807
•
DOI:
- 10.4172/2090-0902.1000130

[9]

Dirac solutions for quaternionic potentials

- J.Math.Phys. 55 (2014) 022301
•
e-Print:
- 1311.6673
•
DOI:
- 10.1063/1.4863903

[10]

: Quaternionic differential operators

S. De Leo
,
G. Ducati

- J.Math.Phys. 42 (2001) 2236-2265

[11]

Violations of quantum mechanics

Stefano De Leo
(
- Campinas State U., IMECC
)
,
Gisele C. Ducati
(
- Campinas State U., IMECC and
- Parana U.
)
,
C. Nishi Celso
(
- Campinas State U.
)

- J.Phys.A 35 (2002) 5411
•
e-Print:
- hep-th/0111143
•
DOI:
- 10.1088/0305-4470/35/26/305

[12]

: Quaternionic bound states

S. De Leo
,
G. Ducati

- J.Phys.A 35 (2005) 3443-3454

[13]

: Quaternionic wave packets

S. De Leo
,
G. Ducati

- J.Math.Phys. 48 (2007) 052111

[14]

The Quaternion scalar field

S. De Leo
(
- Salento U.
)
,
P. Rotelli
(
- Salento U. and
- INFN, Lecce
)

- Phys.Rev.D 45 (1992) 575-579
•
DOI:
- 10.1103/PhysRevD.45.575

[15]

Four-dimensional integrable theories

C. Devchand
(
- Dubna, JINR
)
,
V. Ogievetsky
(
- Dubna, JINR
)

- Gursey String & Symmetries 1994:0169-182,
- In *Istanbul 1994, Proceedings, Strings and symmetries* 169-182, and Preprint - Ogievetskii, V. (94,rec.Oct.) 11 p,
- Lect.Notes Phys. 447 (1995) 169
•
e-Print:
- hep-th/9410147
•
DOI:
- 10.1007/3-540-59163-X_267